Y = x2 – 2x
Axis of Symmetry: _______
Vertex: ________
Domain: _____________
Range: __________
Max or Min: ________
What is your Max or Min? _______
Which way does your parabola
open? Why? ______________________________________

Answer:

The statement is false.

Step-by-step explanation:

If f is increasing and positive on the interval i, then 1/f is decreasing on that interval i.

To see why, consider two points a and b in the interval i, where a < b. Since f is increasing on i, we have f(a) < f(b). This means that 1/f(a) > 1/f(b), since both sides are positive. Therefore, g(x) = 1/f(x) is decreasing on i.

The statement is true. If f is increasing and f(x) > 0 on i, then as x increases, f(x) also increases. This means that 1/f(x) decreases as x increases, since the denominator (f(x)) is getting larger. Therefore, g(x) = 1/f(x) is decreasing on i.

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The inequality is 17 ≥ 3x + 5.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

To express the statement "17 is at least 5 more than 3 times x" as an equation or inequality,

We can start by translating the words "is at least" into the symbol ≥.

Which represents "greater than or equal to."

Now,

We can then translate the words "5 more than" as "+5" and "3 times x" as "3x."

Now,

We can write the equation or inequality as:

17 ≥ 3x + 5

This equation states that 17 is greater than or equal to the result of multiplying x by 3 and then adding 5.

Thus,

The inequality is 17 ≥ 3x + 5.

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Answer:

A) angle

Step-by-step explanation:

This is a definition.

Hello,

\(f(x) = - 5 {x}^{2} + 3\)

\(h(x) = - 5 {x}^{2} + 3 + 5 = - 5 {x}^{2} + 8\)

Answer:

They could sell 10 people one seat and 2 snacks each.

$24+$6+$6=$36

That's be $36x10=$360

Step-by-step explanation:

Answer:

The measure of m∠KNY is;

(D) 105°

Step-by-step explanation:

From the diagram, we have;

The given angle at the circumference = The The angle the arcs makes at the center of the circle

From circle, theorem, angle subtended at the center = Twice the angle subtended at the circumference

Therefore;

Angle ∠D and angle ∠Y = 90°/2 = 45°

Angle ∠O and angle ∠K = 60°/2 = 30°

From angle summation theorem, we have;

m∠KNY + ∠K + ∠Y = 180° (The sum of the interion angles in ΔYNK

∴ m∠KNY = 180° - (∠K + ∠Y)

Plugging in the known values of ∠K and ∠Y gives;

m∠KNY = 180° - (30° + 45°) = 105°

m∠KNY = 105°.

The density of rubbing alcohol with the mass 45 g and volume of 57 ml will be;

⇒ 0.789 g/mL

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The mass of the rubbing alcohol = 45gm

The volume of rubbing alcohol = 57ml

Now,

Since, Density = Mass / Volume

Substitute all the values , we get;

Density of rubbing alcohol = 45 / 57 g/mL

                                         = 0.789 g/mL

Thus, The density of rubbing alcohol with the mass 45 g and volume of 57 ml will be;

⇒ 0.789 g/mL

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Answer:

a = 50

b = 50

c = 80

d = 50

e = 130

Step-by-step explanation:

e = 180 - (25 + 25)   {Angle sum property & It is an isosceles triangle}

    = 180 - 50 = 130

a +e = 180  {Linear pair}

a + 130 = 180

a = 180 - 130

a = 50

d =a   {Vertically opposite angles}

d = 50

c = 180 -(50+ 50 )     {Angle sum property & It is an isosceles triangle}

c = 180 -100

c = 80

a+b + c = 180  {Straight angles}

50 + b + 80 = 180

  b + 130 = 180

          b = 180 - 130

          b = 50

Answer:

141 inch^2

Step-by-step explanation:

13×7= 91 for the rectangle

13-5=8

diameter of circle=8

radius=4

area if circle=4^2 times π

=16×π

=16π

16π+91=141.2654....

to the nearest whole= 141 inch^2 I think

Chevrolet owners are more loyal than owners of different cars, at least based on this sample of 870 Chevrolet owners.

In order to determine if Chevrolet owners are more loyal than owners of different cars, we need to conduct a hypothesis test. Our null hypothesis (H0) would be that there is no significant difference in loyalty between Chevrolet owners and owners of different cars, while our alternative hypothesis (Ha) would be that Chevrolet owners are more loyal. To test this, we can use a one-sample proportion test, since we are comparing the proportion of Chevrolet owners who would buy another Chevrolet (56%) to the proportion of the general consumer population who are loyal to their automobile manufacturer (47%). Using a significance level of 0.05, we can calculate the test statistic and p-value. Our test statistic is: z = (0.56 - 0.47) / √((0.47 × 0.53) / 870) = 4.71
Our p-value is then calculated as the probability of obtaining a z-value of 4.71 or higher:
p = P(Z ≥ 4.71) ≈ 0
Since our p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. Therefore, we can say that Chevrolet owners are more loyal than owners of different cars, at least based on this sample of 870 Chevrolet owners.

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Euler's method is a numerical approximation technique used to solve ordinary differential equations by dividing the interval into small steps and approximating the solution at each step based on the derivative.

To obtain a four-decimal approximation of the value of y(0.5) using Euler's method, we can follow these steps:
1. First, let's define the function \(y' = x^2 + y^2\) and the initial condition      y(0) = 2.

2. Using a numerical solver like Euler's method, we can approximate the value of y at different points.

3. For the first approximation, let's use a step size of h = 0.1. To find the approximation of y(0.5), we need to calculate the values of y at each step using the following formula:

\(y(i + 1) = y(i) + h \left( x(i)^2 + y(i)^2 \right)\)

where i represents the current step and x(i) represents the corresponding x value.

4. Starting with the initial condition y(0) = 2, we can calculate the values of y at each step until we reach x = 0.5. The steps are as follows:

- For i = 0:
    y(0) = 2

- For i = 1:
 x(1) = 0.1,

\(y(1) = y(0) + 0.1 \times (0^2 + 2^2)\)

- For i = 2:
  x(2) = 0.2,

\(y(2) = y(1) + 0.1 \times (0.1^2 + y(1)^2)\)

- Continue this process until we reach x = 0.5.

5. Repeat the above steps with a step size of h = 0.05 to obtain a more accurate approximation of y(0.5).

By following these steps, you should be able to use a numerical solver and Euler's method to obtain a four-decimal approximation of the value of y(0.5) for both h = 0.1 and h = 0.05.

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Answer: 15

Step-by-step explanation: Well first you have to minus 33-18=15

Each type of interviewer should be hired in order to maximize the number of interviews are 0 undergraduate students, 16 graduate students, and 4 faculty members and the maximum number of interviews is 644 according to the statistics given.

If n = the number of interviews, then let x = the number of undergraduate students hired, y = the number of graduate students employed, z = the number of faculty members hired.

The purposeful action is:

maximization of n = 30x + 32y + 33z

The limitations are: x + y + z 20; 100x + 150y + 200z 3200; and 0;

The answer is 644 because x = 0, y = 16, z = 4.

To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics given.

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The methods used to summarize or describe characteristics of data are called descriptive statistics.

Descriptive statistics refers to the branch of statistics that focuses on summarizing and describing the main features or characteristics of a dataset. These statistics provide a way to organize, present, and analyze data to gain insights and understand the data's properties. Here are some key points about descriptive statistics:

Data summarization: Descriptive statistics aim to summarize the main aspects of a dataset, including measures of central tendency (such as mean, median, and mode) that provide information about the typical or average value of the data. Measures of dispersion (such as range, variance, and standard deviation) describe the spread or variability of the data points.

Presentation and visualization: Descriptive statistics often involve presenting data in a meaningful and concise manner. This can be done through various graphical representations, such as histograms, bar charts, box plots, or scatter plots. These visualizations help to provide a clear understanding of the distribution, patterns, and relationships within the data.

Sample statistics and population parameters: Descriptive statistics can be calculated for either a sample or an entire population. Sample statistics are calculated based on data from a subset of the population, while population parameters describe the entire population. Sample statistics, such as sample mean or sample standard deviation, provide estimates or approximations of the population parameters.

Descriptive statistics are widely used in various fields, including social sciences, business, healthcare, finance, and many others. They offer a concise and informative summary of data, enabling researchers, analysts, and decision-makers to gain insights, communicate findings, and make informed decisions based on the characteristics of the data.

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The percentage of American women that have shoe sizes that are at least 11.1 is; 0.0015

Empirical Rule

We are given;

Mean; x' = 8.04

Standard deviation; σ = 1.53

Using the empirical rule, we can have the data either 1, 2, or 3 standard deviations from the mean.

Thus;

At 1 standard deviation from the mean, we have;

8.04 ± 1(1.53)

⇒ (6.52, 8.56)

At 2 standard deviations from the mean, we have;

8.04 ± 2(1.53)

⇒ (5, 11.08)

At 3 standard deviations from the mean, we have;

8.04 ± 3(1.52)

⇒ (3.48, 12.6)

We can see that the one with at least 12,6 is 3 standard deviations from the mean which from the empirical rule is 99.7%

Thus;

percentage of American women have shoe sizes that are at least 12.6 = 100% - 99.7% - 0.15%

P(x ≥ 12.6) = 0.15% = 0.0015

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Answer:

(x+2) (x+2)

Step-by-step explanation:

X^2+4x+4

X^2+2x+2x+4

x(x+2) +2(x+2)

(x+2) (x+2)

Answer:

Step-by-step explanation:

(a) The center of the circle is also the circumcenter of the triangle PQR.

Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:

Sum of the three angles is 360° as cover the full circle.

Each angle measure is:

(b) Each side is 16 cm and the radius is 12 cm.

The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.

The segment MO is:

ΔXYZ is isosceles with:

(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude

Find h:

(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.

Find ∠ZXM:

Find ∠ZOM:

Find the measure of the radius:

Find the measure of the diameter:

The least square estimate for the intercept or \(b_0\) is equal to 6.

What is linear regression?

Regression model interpretation of the intercept isn't always as simple as it seems. The expected mean Y value when all X=0 is the intercept, also referred to as the constant.

Create a regression equation with X as the only predictor to begin.

The expected mean values of Y at that value is the intercept in the event that X occasionally equals 0. That has significance.

The intercept has no inherent value if X never equals 0. In real data, both of these scenarios are typical. A regression model is used in scientific research to analyze the relationship between predictions and responses.

If this is the case and X never equals 0, the intercept is of no interest. It doesn't provide any information regarding the connection between X and Y.

Using formula:

N=5

b0=[(55X15)−(35X15)]/[(5X55)−(15)^2]

b0=(825−525)/(275−225)

b0=300/50

b0=6

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Answer:

Thats a lot of water!

Answer:

≥ means equal or bigger.

So 5x should be equal or bigger than 45.

Which means x can be 9 or 10/11/12...

The given statement that a trinomial is always a higher degree than a monomial is false because greater number of terms does not means higher degree.

A monomial is an algebraic expression with only one term. Or we can say that the representation of a single concept is a monomial.

An example of an unary expression is: 12

A trinomial is an algebraic expression containing three terms. An example of a ternary is: x + y + 7

A trinomial is always of higher degree than a monomial is false statement .

A counterexample can be used to explain why this is wrong. Suppose we have a monomial, 8⁵ and then a trinomial x² + 2x + 3 . This is just a random example. This monomial has a higher degree because 5 is greater than 2. So basically it doesn't matter what the monomial is, if the degree is higher it is just a term than the maximum degree of the trinomial. Just because this has three terms does not mean that the highest degree term is greater than his one term in the monomial.

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Answer:

12

Step-by-step explanation:

The formulated Linear Program aims to minimize the objective function, which is the sum of production and inventory costs minus the revenue from selling the end-of-period inventory at month 4.

In this problem, we need to determine the optimal production and inventory levels over the four-month period to minimize costs and maximize revenue. We can formulate this as a linear programming problem with the following decision variables:

Let x1, x2, x3, x4 represent the production quantities for months 1, 2, 3, and 4, respectively.

Let y1, y2, y3, y4 represent the end-of-month inventory levels for months 1, 2, 3, and 4, respectively.

The objective function we want to minimize is:

Minimize: (5x1 + 8x2 + 4x3 + 7x4) + (2y1 + 2y2 + 2y3) - (15y4)

Subject to the following constraints:

1. Initial inventory: y1 = 15 (given)

2. Production capacity constraints:

  x1 <= 90 (month 1 capacity)

  x2 <= 75 (month 2 capacity)

  x3 <= 80 (month 3 capacity)

  x4 <= 50 (month 4 capacity)

3. Inventory balance equations:

  y1 + x1 - 50 = y2 (month 1)

  y2 + x2 - 65 = y3 (month 2)

  y3 + x3 - 100 = y4 (month 3)

  y4 + x4 - 70 = 0 (month 4, no carryover inventory)

4. Non-negativity constraints:

  x1, x2, x3, x4, y1, y2, y3, y4 ≥ 0

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1. Statement: True

Inverse: True

Contrapositive: True

Converse: True

2. Statement: True

Inverse: True

Contrapositive: True

Converse: True

3. Statement: True

Inverse: True

Contrapositive: True

Converse: True

(i)

Statement: If the difference x - y is even, then x and y are also even.

Inverse: If x and y are not even, then the difference x - y is not even.

Contrapositive: If x and y are not even, then the difference x - y is not even.

Converse: If x and y are even, then the difference x - y is even.

Statement: If a divides b or a divides c, then a divides bc.

Inverse: If a does not divide b and a does not divide c, then a does not divide bc.

Contrapositive: If a does not divide b and a does not divide c, then a does not divide bc.

Converse: If a divides bc, then a divides b or a divides c.

Statement: If x^2 ≥ 100 and x ≥ 0, then x ≥ 10.

Inverse: If x^2 < 100 or x < 0, then x < 10.

Contrapositive: If x^2 < 100 or x < 0, then x < 10.

Converse: If x ≥ 10, then x^2 ≥ 100.

(ii)

For each statement, we need to evaluate the truth values of the statement, inverse, contrapositive, and converse.

Statement: True

Inverse: True

Contrapositive: True

Converse: True

Statement: True

Inverse: True

Contrapositive: True

Converse: True

Statement: True

Inverse: True

Contrapositive: True

Converse: True

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\(9q^2-(3q - 7) +5q= \\\\=9q^2-3q + 7 +5q= \\\\=9q^2+2q + 7\)

For the given probability distribution the probability of rolling less than 5 is 2/3.

The given probability distribution is,

Outcome 1 2 3 4 5 6

The probability of rolling less than 5 is to be determined.

The outcomes which are less than 5 are 1, 2, 3, 4.

P(rolling less than 5) = P(rolling 1) + P(rolling 2) + P(rolling 3) + P(rolling 4)

P(rolling less than 5) = (1/9) + (2/9) + (1/9) + (2/9)

P(rolling less than 5) = (6/9)P(rolling less than 5) = (2/3)

Therefore, the probability of rolling less than 5 is 2/3.

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To show h(t) = |r(t)|², where r(t) is a complex-valued function, we need to first find the magnitude of r(t) and then square it.

Let r(t) = x(t) + i y(t) be a complex-valued function, where x(t) and y(t) are the real and imaginary parts of r(t), respectively. The magnitude of r(t) is given by |r(t)| = √(x(t)² + y(t)²), which is the distance of the point (x(t), y(t)) from the origin in the complex plane.

To find |r(t)|², we simply square the magnitude, i.e., |r(t)|² = (x(t)² + y(t)²).

Therefore, h(t) = |r(t)|² = (x(t)² + y(t)²),

which is the sum of the squares of the real and imaginary parts of r(t).

In the case where r(t) is a real-valued function, i.e., y(t) = 0, then h(t) reduces to h(t) = r(t)².

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Therefore , the solution of the given problem of equation comes out to be value of g is 12 .

In a math equation, the comparable symbol (=) is used to denote equality between two propositions. It is demonstrated that by using mathematical formulas, which have been expressions of reality, different numerical factors can be compared. The equal sign, for instance, splits the integer 12 or the equation y + 6 = 12 to 2 different halves. It is possible to determine how many characters each side of such a symbol has. It's common for symbols to have conflicting meanings.

Here,

Given :

=> g -3 = 9

To find the value of g :

=> g = 9 + 3

=> g = 12

Thus , value of g is 12.

Therefore , the solution of the given problem of equation comes out to be value of g is 12 .

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Answer:

-1.5

Step-by-step explanation:

"h is the amount of right-shift in the translation of the function. Here, the shift is 1.5 units to the left (and 3.5 units down). This make h = -1.5 (and k = -3.5)."